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  • CR: G1.3  (1)
  • Engineering General  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Eigenvalues of graded matrices and the condition numbers of a multiple eigenvalue (1990)
    Springer
    Numerische Mathematik 58 (1990), S. 703-712 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65F15 ; CR: G1.3
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary This paper concerns two closely related topics: the behavior of the eigenvalues of graded matrices and the perturbation of a nondefective multiple eigenvalue. We will show that the eigenvalues of a graded matrix tend to share the graded structure of the matrix and give precise conditions insuring that this tendency is realized. These results are then applied to show that the secants of the canonical angles between the left and right invariant of a multiple eigenvalue tend to characterize its behavior when its matrix is slightly perturbed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01385650
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    On the solution of block Hessenberg systems (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 287-296 
    Details
    ISSN: 1070-5325
    Keywords: block Hessenberg matrix ; block Toeplitz matrix ; linear system ; queue ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper describes a divide-and-conquer strategy for solving block Hessenberg systems. For dense matrices the method is as efficient as Gaussian elimination; however, because it works almost entirely with the original blocks, it is much more efficient for sparse matrices or matrices whose blocks can be generated on the fly. For Toeplitz matrices, the algorithm can be combined with the fast Fourier transform.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nla.1680020309
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    Paper (German National Licenses)
    Fulltext
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